Here is a direct quote from the "Solid Solutions" web site:
It basically shifts the IAT temperature with -20°C. This means that the ECU or computer is fooled and thinks that the temperature is 20 °C colder than in reality. The result is that more fuel will be injected and that is the goal we want! Why -20°C? Calculations and field proven tests have shown that this gives the engine the best technical performance!
You need however to be careful that you don't inject too much fuel. This is the case at temperatures below 0°C! Under 0°C you need to offset the temperature less than 20°C to avoid problems of too rich fuel mixtures which results in bad starting of the engine, too high fuel consumption,...)
To keep the various motorcycle configurations and different temperatures under control, I made a calculation model. I can lay perfectly the offset curve where I want, by using different electronic components. The main component of the ACCELERATOR module™ is a sensor that measures the outside air temperature very well. The other components bent the curve in some temperature ranges, to avoid the problems below zero degrees as mentioned before. The ACCELERATOR module™ is designed to work in all temperature ranges, i.e. from -30°C up to +80°C.
So,
at a given ambient temperature, this device will be indiscriminately adding the same amount of fuel across all RPMs and Throttle positions. The only "intelligence" to these devices is that they have a negative temperature variable that will back off on the fuel addition at colder ambient temps.
As you can see in the below Power Commander stock FJR fuel correction map, generated by DynoJet on a dynamometer from actual data,
the stock FJR1300 does not require additional fuel at all RPMs and Throttle Opening combinations and in fact some of the stock fuel map is already too rich (those cells with negative corrections). Only the areas inside the red circle would benefit from additional fuel. All of the areas outside the circle (and actually some of the smaller positive cells inside the circle) the added fuel would be
detrimental to power and efficiency. By installing one of these Accelerator Modules you will be adding fuel not just to those parts of the fuel map that might benefit from the addition, but also to those areas that are already too rich. That's the indiscriminate part.
For those bikes that retain a functional O2 sensor, the Accelerator module won't do a damned thing whenever the Fuel Injection is operating in closed loop mode (at idle and during steady cruising). In closed loop the lambda feedback will allow the ECU to "undo" the artificial temperature sensor bias that the Accelerator Module introduces. So at those times the module does nothing at all except make it a bit more difficult for the ECU to hit the target A/F ratio. At all other times (i.e. not at idle or steady cruise) the FJR fuel injection runs in "open loop" mode and this dandy module will be steadily adding fuel, only modulated somewhat by the ambient temperature.
The idea that an FJR will somehow get 10% better fuel mileage with one of these modules installed is laughable at best. How could any motorcycle get better fuel mileage by indiscriminately forcing more fuel into the intake?
edit: I should add the following so nobody gets me wrong:
Will adding one of these modules make the off-on throttle transition smoother and reduce the lean surge symptoms that most FJRs seem to exhibit (but only some riders are sensitive to)? Probably yes.
Will adding one of these improve your fuel mileage? Not very likely.
Would I rather use one of these devices or a programmable Power Commander to attain these goals? I would opt for the latter, but clearly the former is a lot cheaper.